import sys
sys.path.append("..")

from sympy import exp,log,Symbol,Rational,sin,limit, sqrt,oo

x=Symbol("x")
a=Symbol("a")
h=Symbol("h")

def sqrt3(x):
    return x**Rational(1,3)

def show(computed, correct):
    print "computed:",computed,"correct:",correct

show( limit(sqrt(x**2-5*x+6)-x,x,oo) , -Rational(5)/2 )
show( limit(x*(sqrt(x**2+1)-x),x,oo) , Rational(1)/2 )
show( limit(x-sqrt3(x**3-1),x,oo) , Rational(0) )
show( limit(log(1+exp(x))/x,x,-oo) , Rational(0) )
show( limit(log(1+exp(x))/x,x,oo) , Rational(1) )
show( limit(sin(3*x)/x,x,0) , Rational(3) )
show( limit(sin(5*x)/sin(2*x),x,0) , Rational(5)/2 )
show( limit(((x-1)/(x+1))**x,x,oo) , exp(-2))
